Non-Abelian quasiparticles are collective excitations of topological phases that exhibit exotic exchange statistics. These include non-Abelian anyons, whose exchange statistics are governed by higher-dimensional representations of the braid group. Such quasiparticles collectively possess a multi-dimensional, non-local (topological) state space that is essentially immune to local perturbations. This property makes non-Abelian topological phases appealing platforms for quantum information processing, as they allow for topologically protected quantum computation (TQC). In the TQC approach, computational gates may be generated through topological operations, such as braiding exchanges of quasiparticles, in which case they are also topologically protected. The physical implementation of such protected gates poses one of the most significant challenges for realization of TQC.
The initial conception of TQC envisioned physically translocating non-Abelian quasiparticles to perform braiding operations as the primary means of generating gates. Proposals for moving quasiparticles include simply dragging them around (e.g., with a Scanning Tunneling Microscope (STM) tip, if they are electrically charged) and a “bucket brigade” series of induced hoppings from one site to the next, originating at one location and terminating at another. A subsequent proposal, known as “measurement-only TQC” (MOTQC), introduced methods of effectively generating braiding transformations on the state space, without physically moving the anyons associated with the state space.